I have a watch that does that. Every so often I get it into a mode where it "meeps" every hour, and I have to find and read the manual (no small task, especially the finding) to work out how to switch the hourly "meep" off.
And they always seem to make the "meeps" at a frequency where your ears are not very directional...
And of course it's always at night since batteries operate less efficiently at lower temperatures. Perhaps the need to latch the low battery trigger until a light sensor indicates it's no longer night time? ;-)
My wife bought me a watch for Christmas -- it looks like the control panel for a 747 -- it has so many knobs and dials that it's difficult to find the ones that tell the time (grin)
There's some sort of alarm function that goes off at 2:00am every morning -- I have no idea where I put the instructions -- so every night before I go to bed I have to bury the watch at the bottom of my sock drawer...
... I tell you, t=you wouldn't believe my life if you saw it as a sitcom on TV :-)
I had a watch like that, but the instructions didn't seem affect the way the watch worked. It also just beeped in the middle of the night. It aslo had a compass (just a magnet on a pivot) and it couldn't find north. It always pointed in the same direction, just not north. Uswed to tell the time OK, but I am not sure which time zone.
I have an alarm clock that every now and then ignores the switch setting (cured by a shpritz of switch cleaner) and beeps when it is off. I normally get up before the alarm anyway and turn it off. But it gets the wife... (nasty chuckle).
I remember long ago when every night about 3am my fire alarm would actually go off (no fires, though). I replaced the batteries, checked the wiring, everything I could think of. One night I was so annoyed I threw a shoe at it (luckily a slipper, not a boot). A cockroach fell out. A shot of Raid fixed the problem.
In Arizona, we have crickets that lead to midnight-annoyance.... but crickets are self-propelled.
When you look at those lights, just imagine that each is probably 25mW. You own ten, I own ten, everybody owns 10, and there are 300M Americans. That makes 75MW of glowing LEDs!!!
I was spending the night in my sister's guest/junk room, about to fall asleep when I hear what sounds like a cricket chirp. Try to ignore it, but it keeps repeating. Grab my shoe and try to find him, but hard to localize the sound, too brief.
Get my watch and time the period between chirps. Exactly the same, so it's artificial.
Knowing when the next chirp will be, I eventually find the general area of the sound: a group of moving boxes. After searching through several, I finally discover a smoke detector carefully packed away, battery on its last legs...
A truly evil prank: hide a detector with an aging battery where someone will never find it.